No CrossRef data available.
Article contents
Krull Dimension of Injective Modules Over Commutative Noetherian Rings
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $R$ be a commutative Noetherian integral domain with field of fractions $Q$. Generalizing a forty-year-old theorem of E. Matlis, we prove that the $R$-module $Q/R$ (or $Q$) has Krull dimension if and only if $R$ is semilocal and one-dimensional. Moreover, if $X$ is an injective module over a commutative Noetherian ring such that $X$ has Krull dimension, then the Krull dimension of $X$ is at most 1.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2005